This paper deals with the relationship between the elastic anisotropic coefficients and  the porosity of the gas coal samples. The result shows that the value of anisotropic coefficient is to a certain extent related to porosity. This paper simulates the one-order stress-velocity equation with the staggered grid high-order difference method, and analyzes the stability and boundary conditions.  The simulations of Thomsen show that, in the wave simulation with the staggered-grid high-order difference method, ε denotes the anisotropic degree of of P-wave, and δ is the changing degree of transverse and vertical anisotropy of P-wave.